Analisis Pertumbuhan Ekonomi Menggunakan Metode VECM
## Warning: package 'readxl' was built under R version 4.3.3## Warning: package 'tseries' was built under R version 4.3.3## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo## Warning: package 'urca' was built under R version 4.3.3## Warning: package 'vars' was built under R version 4.3.3## Loading required package: MASS## Loading required package: strucchange## Warning: package 'strucchange' was built under R version 4.3.3## Loading required package: zoo## Warning: package 'zoo' was built under R version 4.3.3##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## Loading required package: sandwich## Warning: package 'sandwich' was built under R version 4.3.3## Loading required package: lmtest## Warning: package 'lmtest' was built under R version 4.3.3## Warning: package 'tsDyn' was built under R version 4.3.3Eksplorasi DATA
## tibble [56 × 6] (S3: tbl_df/tbl/data.frame)
## $ Quarter: chr [1:56] "2011 Q1" "2011 Q2" "20 11 Q3" "2011 Q4" ...
## $ X1 : chr [1:56] "124.29" "124.29" "115.42" "125.36" ...
## $ X2 : num [1:56] 5192 5776 5359 5565 6751 ...
## $ X3 : chr [1:56] "6.65%" "5.54%" "4.61%" "3.79%" ...
## $ X4 : num [1:56] 7.905 1.805 -14.084 0.821 4.563 ...
## $ Y : chr [1:56] "1,834,355.10" "1,928,233.00" "2,053,745.40" "2,015,392.50" ...df <- data.frame(
X1 = as.numeric(data$X1),
X2 = as.numeric(data$X2),
X3 = as.numeric(gsub("%", "", data$X3))/100,
X4 = as.numeric(data$X4),
Y = as.numeric(gsub(",", "", data$Y))
)
df_ts <- ts(df, start=c(2011,1), frequency=4)
# Tambahkan rownames dengan nama quarter
quarters <- data$Quarter
df_ts_named <- df_ts
dimnames(df_ts_named) <- list(quarters, colnames(df_ts))
df_ts_named## X1 X2 X3 X4 Y
## 2011 Q1 124.29 5192.46 0.0665 7.9051499 1834355
## 2011 Q2 124.29 5775.96 0.0554 1.8051534 1928233
## 2011 Q3 115.42 5358.85 0.0461 -14.0837126 2053745
## 2011 Q4 125.36 5564.79 0.0379 0.8214517 2015393
## 2012 Q1 138.74 6751.16 0.0397 4.5630174 2061338
## 2012 Q2 131.61 5776.83 0.0453 -5.3854231 2162037
## 2012 Q3 143.96 5563.10 0.0431 2.9022243 2223642
## 2012 Q4 144.99 5666.23 0.0430 -0.7723623 2168688
## 2013 Q1 162.64 8540.46 0.0590 10.9412399 2235289
## 2013 Q2 164.24 9437.78 0.0590 -4.2742751 2342590
## 2013 Q3 145.15 9350.89 0.0840 -6.3812527 2491159
## 2013 Q4 143.71 9432.19 0.0838 -5.2420615 2477098
## 2014 Q1 157.35 8918.50 0.0732 7.9099114 2506300
## 2014 Q2 159.75 9384.47 0.0670 0.7939837 2618947
## 2014 Q3 166.76 9690.21 0.0453 0.9585757 2746762
## 2014 Q4 168.64 10198.79 0.0836 2.6996493 2697695
## 2015 Q1 174.10 12035.97 0.0638 4.3345181 2728181
## 2015 Q2 157.92 9303.46 0.0726 -3.4554756 2867948
## 2015 Q3 134.39 10108.49 0.0683 -12.0482329 2990645
## 2015 Q4 145.06 11019.43 0.0335 3.0937022 2939559
## 2016 Q1 155.91 9470.14 0.0445 4.9881261 2929269
## 2016 Q2 165.94 9928.47 0.0345 3.6802120 3073537
## 2016 Q3 176.93 12087.00 0.0307 2.8529579 3205019
## 2016 Q4 172.08 14914.63 0.0302 -2.3204992 3193904
## 2017 Q1 180.49 16123.54 0.0361 5.1757617 3228172
## 2017 Q2 185.22 18914.54 0.0437 2.5400595 3366787
## 2017 Q3 184.23 21427.72 0.0372 1.0256911 3504139
## 2017 Q4 189.86 28311.77 0.0361 5.8255547 3490728
## 2018 Q1 183.59 31108.82 0.0340 -6.3073469 3510363
## 2018 Q2 173.25 32167.28 0.0312 -3.2589330 3686836
## 2018 Q3 178.09 31797.51 0.0288 0.6756575 3842343
## 2018 Q4 184.00 34491.17 0.0313 6.2220812 3799214
## 2019 Q1 190.17 37114.19 0.0248 -0.9830139 3782618
## 2019 Q2 186.01 33056.75 0.0328 -1.4982921 3964075
## 2019 Q3 188.93 55543.29 0.0339 -3.4645176 4067358
## 2019 Q4 187.73 53735.58 0.0272 1.1434865 4018606
## 2020 Q1 133.99 57420.96 0.0296 -23.5876802 3923348
## 2020 Q2 144.91 58069.05 0.0196 4.0070817 3690742
## 2020 Q3 143.81 71649.52 0.0142 -5.4293221 3897852
## 2020 Q4 177.48 74367.44 0.0168 16.5912995 3931411
## 2021 Q1 176.89 79440.23 0.0137 2.1010346 3972933
## 2021 Q2 171.95 40325.60 0.0133 -0.1689567 4178022
## 2021 Q3 181.54 41313.64 0.0160 3.5732878 4327384
## 2021 Q4 189.02 44004.18 0.0187 -0.1497417 4498413
## 2022 Q1 199.91 43233.00 0.0264 6.6397231 4508663
## 2022 Q2 200.39 40859.70 0.0435 -4.3897351 4898032
## 2022 Q3 204.10 40342.63 0.0595 1.2901518 5066968
## 2022 Q4 217.73 40605.11 0.0551 -3.4973073 5114797
## 2023 Q1 211.27 42650.15 0.0497 -0.4980013 5071497
## 2023 Q2 198.85 42947.06 0.0352 -3.6704783 5223290
## 2023 Q3 216.99 43110.74 0.0228 0.1230639 5294903
## 2023 Q4 212.64 42775.16 0.0261 7.7099202 5302658
## 2024 Q1 209.64 43719.10 0.0305 1.1219572 5288577
## 2024 Q2 209.27 44728.93 0.0251 -2.3585193 5536589
## 2024 Q3 226.63 47293.47 0.0184 3.7510888 5638869
## 2024 Q4 215.65 50547.54 0.0157 -6.5238803 5674930Uji Akar Unit
adf_results <- lapply(df_ts_named, function(x) ur.df(x, type="trend", selectlags="AIC"))
lapply(adf_results, summary)## $X1
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -53.207 -2.775 1.593 6.817 16.753
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 52.4345 15.7112 3.337 0.00160 **
## z.lag.1 -0.3814 0.1165 -3.273 0.00194 **
## tt 0.5208 0.1932 2.696 0.00953 **
## z.diff.lag 0.1007 0.1421 0.709 0.48186
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 11.89 on 50 degrees of freedom
## Multiple R-squared: 0.1839, Adjusted R-squared: 0.1349
## F-statistic: 3.755 on 3 and 50 DF, p-value: 0.01648
##
##
## Value of test-statistic is: -3.2725 4.0109 5.3617
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -4.04 -3.45 -3.15
## phi2 6.50 4.88 4.16
## phi3 8.73 6.49 5.47
##
##
## $X2
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33450 -1629 -817 924 21304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 594.00888 1900.27262 0.313 0.7559
## z.lag.1 -0.16812 0.08390 -2.004 0.0505 .
## tt 177.00896 107.26145 1.650 0.1052
## z.diff.lag -0.03152 0.14196 -0.222 0.8252
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6639 on 50 degrees of freedom
## Multiple R-squared: 0.08715, Adjusted R-squared: 0.03238
## F-statistic: 1.591 on 3 and 50 DF, p-value: 0.2032
##
##
## Value of test-statistic is: -2.0039 1.6815 2.0099
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -4.04 -3.45 -3.15
## phi2 6.50 4.88 4.16
## phi3 8.73 6.49 5.47
##
##
## $X3
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.028900 -0.005763 -0.001803 0.003317 0.036680
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.0150524 0.0069803 2.156 0.0359 *
## z.lag.1 -0.2559776 0.1039069 -2.464 0.0172 *
## tt -0.0001938 0.0001181 -1.640 0.1072
## z.diff.lag -0.0493038 0.1402509 -0.352 0.7267
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01074 on 50 degrees of freedom
## Multiple R-squared: 0.137, Adjusted R-squared: 0.08526
## F-statistic: 2.647 on 3 and 50 DF, p-value: 0.05909
##
##
## Value of test-statistic is: -2.4635 2.1572 3.0503
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -4.04 -3.45 -3.15
## phi2 6.50 4.88 4.16
## phi3 8.73 6.49 5.47
##
##
## $X4
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -23.7353 -3.2693 0.2378 3.7062 15.6093
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.44554 1.79125 -0.249 0.805
## z.lag.1 -1.22639 0.21416 -5.726 5.81e-07 ***
## tt 0.01724 0.05520 0.312 0.756
## z.diff.lag 0.05022 0.14049 0.357 0.722
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.31 on 50 degrees of freedom
## Multiple R-squared: 0.5799, Adjusted R-squared: 0.5547
## F-statistic: 23.01 on 3 and 50 DF, p-value: 1.692e-09
##
##
## Value of test-statistic is: -5.7264 10.9491 16.3973
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -4.04 -3.45 -3.15
## phi2 6.50 4.88 4.16
## phi3 8.73 6.49 5.47
##
##
## $Y
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression trend
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -323341 -71401 19207 62877 288144
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.372e+05 1.395e+05 2.417 0.0193 *
## z.lag.1 -1.797e-01 8.363e-02 -2.149 0.0365 *
## tt 1.273e+04 5.610e+03 2.269 0.0276 *
## z.diff.lag 1.310e-01 1.440e-01 0.910 0.3672
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 99930 on 50 degrees of freedom
## Multiple R-squared: 0.1007, Adjusted R-squared: 0.04674
## F-statistic: 1.866 on 3 and 50 DF, p-value: 0.1473
##
##
## Value of test-statistic is: -2.1488 7.1874 2.7489
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau3 -4.04 -3.45 -3.15
## phi2 6.50 4.88 4.16
## phi3 8.73 6.49 5.47Differencing L(1)
df_diff <- diff(df_ts_named)
colnames(df_diff) <- colnames(df_ts_named)
rownames(df_diff) <- rownames(df_ts_named)[-1]
adf_diff_results <- lapply(df_diff, function(x) ur.df(x, type="drift", selectlags="AIC"))
lapply(adf_diff_results, summary)## $X1
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -55.792 -5.028 1.314 6.682 32.688
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3099 1.8093 1.277 0.208
## z.lag.1 -1.2393 0.2070 -5.987 2.3e-07 ***
## z.diff.lag 0.1324 0.1424 0.930 0.357
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.9 on 50 degrees of freedom
## Multiple R-squared: 0.555, Adjusted R-squared: 0.5372
## F-statistic: 31.18 on 2 and 50 DF, p-value: 1.621e-09
##
##
## Value of test-statistic is: -5.9865 17.9218
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.51 -2.89 -2.58
## phi1 6.70 4.71 3.86
##
##
## $X2
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39487 -947 -33 1890 21052
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 936.602023 961.296969 0.974 0.335
## z.lag.1 -1.106752 0.211904 -5.223 3.43e-06 ***
## z.diff.lag -0.009662 0.141671 -0.068 0.946
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6898 on 50 degrees of freedom
## Multiple R-squared: 0.5584, Adjusted R-squared: 0.5407
## F-statistic: 31.61 on 2 and 50 DF, p-value: 1.338e-09
##
##
## Value of test-statistic is: -5.2229 13.6439
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.51 -2.89 -2.58
## phi1 6.70 4.71 3.86
##
##
## $X3
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.035807 -0.006023 -0.000582 0.003830 0.035736
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.0006183 0.0015489 -0.399 0.691
## z.lag.1 -1.0758172 0.2139046 -5.029 6.71e-06 ***
## z.diff.lag -0.0991756 0.1388432 -0.714 0.478
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.01122 on 50 degrees of freedom
## Multiple R-squared: 0.6032, Adjusted R-squared: 0.5873
## F-statistic: 38 on 2 and 50 DF, p-value: 9.209e-11
##
##
## Value of test-statistic is: -5.0294 12.6542
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.51 -2.89 -2.58
## phi1 6.70 4.71 3.86
##
##
## $X4
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22.0692 -4.4249 -0.6795 3.0811 21.0145
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1283 1.0256 0.125 0.901
## z.lag.1 -1.8983 0.2303 -8.244 7e-11 ***
## z.diff.lag 0.2052 0.1309 1.567 0.123
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 7.465 on 50 degrees of freedom
## Multiple R-squared: 0.808, Adjusted R-squared: 0.8003
## F-statistic: 105.2 on 2 and 50 DF, p-value: < 2.2e-16
##
##
## Value of test-statistic is: -8.2437 34.0157
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.51 -2.89 -2.58
## phi1 6.70 4.71 3.86
##
##
## $Y
##
## ###############################################
## # Augmented Dickey-Fuller Test Unit Root Test #
## ###############################################
##
## Test regression drift
##
##
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
##
## Residuals:
## Min 1Q Median 3Q Max
## -326990 -60836 1837 54901 353988
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 85130.8612 18976.6868 4.486 4.27e-05 ***
## z.lag.1 -1.2407 0.1865 -6.651 2.11e-08 ***
## z.diff.lag 0.2941 0.1350 2.179 0.0341 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 100300 on 50 degrees of freedom
## Multiple R-squared: 0.5258, Adjusted R-squared: 0.5069
## F-statistic: 27.72 on 2 and 50 DF, p-value: 7.912e-09
##
##
## Value of test-statistic is: -6.6511 22.1259
##
## Critical values for test statistics:
## 1pct 5pct 10pct
## tau2 -3.51 -2.89 -2.58
## phi1 6.70 4.71 3.86Penentuan Panjang lag optimal
df_diff_scaled <- scale(df_diff)
lag <- VARselect(df_diff_scaled, lag.max = 8, type = "const")
p_lag <- as.numeric(lag$selection["AIC(n)"])
lag$selection## AIC(n) HQ(n) SC(n) FPE(n)
## 8 8 8 8Uji Kointegrasi
df_level_var <- as.data.frame(df_ts_named)
colnames(df_level_var) <- c("SS", "RD", "Inflasi", "IHSGr", "PDB")
cat("Variables:", colnames(df_level_var), "\n")## Variables: SS RD Inflasi IHSGr PDB## 'data.frame': 56 obs. of 5 variables:
## $ SS : num 124 124 115 125 139 ...
## $ RD : num 5192 5776 5359 5565 6751 ...
## $ Inflasi: num 0.0665 0.0554 0.0461 0.0379 0.0397 0.0453 0.0431 0.043 0.059 0.059 ...
## $ IHSGr : num 7.905 1.805 -14.084 0.821 4.563 ...
## $ PDB : num 1834355 1928233 2053745 2015393 2061338 ...df_scaled <- scale(df_level_var)
johansen_test <- ca.jo(df_scaled, type="trace", ecdet="const", K = 2)
summary(johansen_test)##
## ######################
## # Johansen-Procedure #
## ######################
##
## Test type: trace statistic , without linear trend and constant in cointegration
##
## Eigenvalues (lambda):
## [1] 6.272718e-01 3.987427e-01 3.416712e-01 1.917654e-01 6.757313e-02
## [6] 2.563575e-17
##
## Values of teststatistic and critical values of test:
##
## test 10pct 5pct 1pct
## r <= 4 | 3.78 7.52 9.24 12.97
## r <= 3 | 15.27 17.85 19.96 24.60
## r <= 2 | 37.85 32.00 34.91 41.07
## r <= 1 | 65.32 49.65 53.12 60.16
## r = 0 | 118.61 71.86 76.07 84.45
##
## Eigenvectors, normalised to first column:
## (These are the cointegration relations)
##
## SS.l2 RD.l2 Inflasi.l2 IHSGr.l2 PDB.l2 constant
## SS.l2 1.00000000 1.00000000 1.0000000 1.0000000 1.00000 1.0000000
## RD.l2 0.19786327 0.47777367 0.2394901 -1.4770842 90.52194 1.5071532
## Inflasi.l2 -0.11780270 0.11725562 -0.2959037 -1.7877029 -32.40224 1.0153027
## IHSGr.l2 -1.89164145 -0.08726961 -0.1484687 -0.1915079 -16.73856 -0.7157287
## PDB.l2 -0.98401311 -1.10488887 -1.3408885 -0.7881501 -88.35949 -5.2911294
## constant -0.08361057 0.17005768 -0.7405340 0.6246780 3.60423 0.1690477
##
## Weights W:
## (This is the loading matrix)
##
## SS.l2 RD.l2 Inflasi.l2 IHSGr.l2 PDB.l2
## SS.d 0.002311096 -0.63288512 -0.11498314 0.019391242 4.890111e-04
## RD.d 0.130875418 -0.07817508 -0.01610687 0.058073134 -7.292602e-04
## Inflasi.d 0.056264902 0.16638160 0.29190578 0.112594453 9.458949e-04
## IHSGr.d 0.734826548 -1.32802820 -0.19743527 -0.006951971 1.554248e-03
## PDB.d -0.033697868 0.06501222 -0.06170546 0.012700568 9.377307e-05
## constant
## SS.d 4.137705e-17
## RD.d -1.414658e-17
## Inflasi.d -4.658815e-17
## IHSGr.d 1.965326e-17
## PDB.d -4.259199e-18Estimasi VECM
## Response SS.d :
##
## Call:
## lm(formula = SS.d ~ ect1 + SS.dl1 + RD.dl1 + Inflasi.dl1 + IHSGr.dl1 +
## PDB.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.90887 -0.21828 0.03225 0.26994 0.97000
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 0.0023111 0.0837606 0.028 0.9781
## SS.dl1 -0.1931799 0.3042747 -0.635 0.5285
## RD.dl1 0.0931194 0.1971841 0.472 0.6389
## Inflasi.dl1 -0.0008441 0.1092996 -0.008 0.9939
## IHSGr.dl1 0.0471118 0.1301991 0.362 0.7191
## PDB.dl1 1.3055252 0.6430401 2.030 0.0479 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4642 on 48 degrees of freedom
## Multiple R-squared: 0.08768, Adjusted R-squared: -0.02635
## F-statistic: 0.7689 on 6 and 48 DF, p-value: 0.5981
##
##
## Response RD.d :
##
## Call:
## lm(formula = RD.d ~ ect1 + SS.dl1 + RD.dl1 + Inflasi.dl1 + IHSGr.dl1 +
## PDB.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.40638 -0.06926 0.03015 0.15054 0.86044
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 0.13088 0.05345 2.448 0.0181 *
## SS.dl1 0.12543 0.19417 0.646 0.5214
## RD.dl1 -0.06727 0.12583 -0.535 0.5954
## Inflasi.dl1 0.05583 0.06975 0.800 0.4274
## IHSGr.dl1 -0.04514 0.08309 -0.543 0.5894
## PDB.dl1 0.61091 0.41036 1.489 0.1431
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2962 on 48 degrees of freedom
## Multiple R-squared: 0.2818, Adjusted R-squared: 0.1921
## F-statistic: 3.14 on 6 and 48 DF, p-value: 0.01119
##
##
## Response Inflasi.d :
##
## Call:
## lm(formula = Inflasi.d ~ ect1 + SS.dl1 + RD.dl1 + Inflasi.dl1 +
## IHSGr.dl1 + PDB.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.50513 -0.38820 -0.08304 0.17085 1.74218
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 0.05626 0.10411 0.540 0.591
## SS.dl1 0.70621 0.37819 1.867 0.068 .
## RD.dl1 -0.25963 0.24508 -1.059 0.295
## Inflasi.dl1 -0.13128 0.13585 -0.966 0.339
## IHSGr.dl1 -0.17324 0.16183 -1.071 0.290
## PDB.dl1 -0.28223 0.79924 -0.353 0.726
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5769 on 48 degrees of freedom
## Multiple R-squared: 0.14, Adjusted R-squared: 0.03252
## F-statistic: 1.302 on 6 and 48 DF, p-value: 0.2743
##
##
## Response IHSGr.d :
##
## Call:
## lm(formula = IHSGr.d ~ ect1 + SS.dl1 + RD.dl1 + Inflasi.dl1 +
## IHSGr.dl1 + PDB.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.1122 -0.6259 -0.0434 0.6363 2.7712
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 0.7348 0.2001 3.672 0.000604 ***
## SS.dl1 0.7861 0.7270 1.081 0.284951
## RD.dl1 0.1890 0.4711 0.401 0.690010
## Inflasi.dl1 -0.2004 0.2611 -0.767 0.446681
## IHSGr.dl1 -1.2937 0.3111 -4.159 0.000131 ***
## PDB.dl1 0.4072 1.5363 0.265 0.792087
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.109 on 48 degrees of freedom
## Multiple R-squared: 0.5202, Adjusted R-squared: 0.4602
## F-statistic: 8.673 on 6 and 48 DF, p-value: 2.1e-06
##
##
## Response PDB.d :
##
## Call:
## lm(formula = PDB.d ~ ect1 + SS.dl1 + RD.dl1 + Inflasi.dl1 + IHSGr.dl1 +
## PDB.dl1 - 1, data = data.mat)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.08402 -0.01450 0.02848 0.07102 0.30392
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## ect1 -0.033698 0.018030 -1.869 0.0677 .
## SS.dl1 -0.007775 0.065497 -0.119 0.9060
## RD.dl1 -0.023928 0.042445 -0.564 0.5756
## Inflasi.dl1 0.006613 0.023527 0.281 0.7799
## IHSGr.dl1 0.042145 0.028026 1.504 0.1392
## PDB.dl1 0.352664 0.138419 2.548 0.0141 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.09992 on 48 degrees of freedom
## Multiple R-squared: 0.2783, Adjusted R-squared: 0.1881
## F-statistic: 3.085 on 6 and 48 DF, p-value: 0.01233Uji Stabilitas
# Cek stabilitas
p_lag_level <- p_lag - 1
var_model <- VAR(df_level_var, p = p_lag_level, type = "const")
# Check stability
cat("Model Roots:\n")## Model Roots:## [1] 1.0043572 0.9918262 0.9918262 0.9746900 0.9746900 0.9616932 0.9616932
## [8] 0.9610912 0.9610912 0.9592556 0.9592556 0.9588253 0.9588253 0.9575513
## [15] 0.9575513 0.9557252 0.9557252 0.9458494 0.9458494 0.9288141 0.9288141
## [22] 0.9031963 0.8976925 0.8976925 0.8835030 0.8835030 0.8805860 0.8805860
## [29] 0.8770121 0.8648712 0.8648712 0.6301003 0.5975605 0.5975605 0.4919370##
## All roots < 1? FALSEUji Kausalitas
granger_results <- lapply(colnames(df_level_var), function(v) {
causality(var_model, cause = v)$Granger
})
names(granger_results) <- colnames(df_level_var)
granger_results## $SS
##
## Granger causality H0: SS do not Granger-cause RD Inflasi IHSGr PDB
##
## data: VAR object var_model
## F-Test = 1.2241, df1 = 28, df2 = 65, p-value = 0.2484
##
##
## $RD
##
## Granger causality H0: RD do not Granger-cause SS Inflasi IHSGr PDB
##
## data: VAR object var_model
## F-Test = 2.9261, df1 = 28, df2 = 65, p-value = 0.0001901
##
##
## $Inflasi
##
## Granger causality H0: Inflasi do not Granger-cause SS RD IHSGr PDB
##
## data: VAR object var_model
## F-Test = 2.1928, df1 = 28, df2 = 65, p-value = 0.00484
##
##
## $IHSGr
##
## Granger causality H0: IHSGr do not Granger-cause SS RD Inflasi PDB
##
## data: VAR object var_model
## F-Test = 1.1373, df1 = 28, df2 = 65, p-value = 0.3278
##
##
## $PDB
##
## Granger causality H0: PDB do not Granger-cause SS RD Inflasi IHSGr
##
## data: VAR object var_model
## F-Test = 1.8467, df1 = 28, df2 = 65, p-value = 0.02187IMPULSE RESPONSE FUNCTION (IRF)
irf_result <- irf(var_from_vecm,
impulse = variables,
response = variables,
n.ahead = 10,
boot = TRUE,
ci = 0.95)
plot(irf_result)
# Forcast Eror Variance Decomposition (FEVD)
## $SS
## SS RD Inflasi IHSGr PDB
## [1,] 1.0000000 0.0000000 0.000000e+00 0.00000000 0.0000000
## [2,] 0.7281873 0.0289293 3.775027e-05 0.07817614 0.1646696
## [3,] 0.5664762 0.1983509 1.217145e-03 0.07706022 0.1568955
## [4,] 0.5019173 0.2490619 4.068439e-02 0.06871174 0.1396248
## [5,] 0.4726017 0.2775177 3.995165e-02 0.07805908 0.1318699
## [6,] 0.4692073 0.2736820 3.970868e-02 0.07752598 0.1398760
## [7,] 0.4645187 0.2701913 4.228852e-02 0.07997328 0.1430282
## [8,] 0.4408226 0.2783522 5.621764e-02 0.07727585 0.1473317
## [9,] 0.4370682 0.2766407 5.738076e-02 0.08372912 0.1451812
## [10,] 0.4183811 0.2836891 5.524071e-02 0.08923495 0.1534541
##
## $RD
## SS RD Inflasi IHSGr PDB
## [1,] 0.04122455 0.9587754 0.00000000 0.0000000000 0.000000000
## [2,] 0.07088983 0.8854233 0.03411995 0.0002910951 0.009275824
## [3,] 0.19131300 0.7563915 0.02358425 0.0205411327 0.008170079
## [4,] 0.22076291 0.6998317 0.01867628 0.0220728123 0.038656275
## [5,] 0.25357107 0.6322477 0.05208235 0.0264472291 0.035651657
## [6,] 0.25240161 0.5722023 0.09809642 0.0254687898 0.051830913
## [7,] 0.23652055 0.5486132 0.11954350 0.0233689865 0.071953805
## [8,] 0.24260749 0.5141950 0.12895891 0.0393513330 0.074887268
## [9,] 0.22638332 0.4466874 0.18219145 0.0472396857 0.097498177
## [10,] 0.22412951 0.3736586 0.19651266 0.0730491993 0.132649981
##
## $Inflasi
## SS RD Inflasi IHSGr PDB
## [1,] 0.03478859 0.01381851 0.9513929 0.00000000 0.000000000
## [2,] 0.02662640 0.02602875 0.8557683 0.08675067 0.004825843
## [3,] 0.10521774 0.02532673 0.7738347 0.08374458 0.011876291
## [4,] 0.13161678 0.07250585 0.7088789 0.07416453 0.012833923
## [5,] 0.12707545 0.27034335 0.5262784 0.05904592 0.017256872
## [6,] 0.13406094 0.34094918 0.4587140 0.05140591 0.014869971
## [7,] 0.12247079 0.36420962 0.4220725 0.07465556 0.016591550
## [8,] 0.12229073 0.36495542 0.4193281 0.07397661 0.019449121
## [9,] 0.16246275 0.33473818 0.3922929 0.07577431 0.034731886
## [10,] 0.17080954 0.30077184 0.3710133 0.08119550 0.076209808
##
## $IHSGr
## SS RD Inflasi IHSGr PDB
## [1,] 0.9137473 0.002712839 0.003916223 0.07962362 0.0000000
## [2,] 0.7112095 0.019619179 0.006145066 0.08286264 0.1801636
## [3,] 0.6347732 0.118768909 0.006169241 0.07416367 0.1661250
## [4,] 0.6069815 0.137891082 0.063048782 0.06353695 0.1285417
## [5,] 0.5851700 0.130396450 0.092783471 0.06375096 0.1278992
## [6,] 0.5464605 0.178116891 0.088166012 0.06220221 0.1250544
## [7,] 0.5401426 0.172128354 0.105065017 0.05966817 0.1229959
## [8,] 0.5160909 0.170236127 0.102796466 0.07400149 0.1368750
## [9,] 0.4988781 0.166277605 0.110583675 0.08154810 0.1427125
## [10,] 0.4848540 0.185832017 0.106779493 0.08089597 0.1416385
##
## $PDB
## SS RD Inflasi IHSGr PDB
## [1,] 0.07207455 0.3485492 0.015653326 9.953849e-06 0.5637130
## [2,] 0.43110634 0.2923672 0.006186715 5.230683e-03 0.2651091
## [3,] 0.50357180 0.2424045 0.006088616 4.400393e-02 0.2039312
## [4,] 0.48049553 0.2702484 0.004512831 6.924681e-02 0.1754964
## [5,] 0.42577365 0.3192087 0.012362000 6.543285e-02 0.1772228
## [6,] 0.41618436 0.3328644 0.016896287 7.546978e-02 0.1585852
## [7,] 0.44476669 0.3123080 0.015658512 8.148412e-02 0.1457827
## [8,] 0.43911751 0.3022100 0.016710765 9.479208e-02 0.1471696
## [9,] 0.43433878 0.2959900 0.021145242 9.589008e-02 0.1526359
## [10,] 0.43273521 0.2917161 0.024252372 9.664125e-02 0.1546551ECM Analysis
## Long-run equilibrium relationships (Cointegrating vectors):##
## Call:
## lm(formula = substitute(form1), data = data.mat)
##
## Coefficients:
## SS.d RD.d Inflasi.d IHSGr.d PDB.d
## ect1 0.0023111 0.1308754 0.0562649 0.7348265 -0.0336979
## SS.dl1 -0.1931799 0.1254267 0.7062060 0.7860843 -0.0077749
## RD.dl1 0.0931194 -0.0672729 -0.2596284 0.1890338 -0.0239277
## Inflasi.dl1 -0.0008441 0.0558348 -0.1312762 -0.2003584 0.0066129
## IHSGr.dl1 0.0471118 -0.0451419 -0.1732431 -1.2936517 0.0421446
## PDB.dl1 1.3055252 0.6109090 -0.2822330 0.4072394 0.3526638# Extract error correction term
ec_term <- vecm_model$rlm$residuals
cat("\nError correction residuals:\n")##
## Error correction residuals:## SS.d RD.d Inflasi.d IHSGr.d PDB.d
## 2011 Q1 -0.37865983 0.312081504 -0.535616077 -1.77513190 0.027892941
## 2011 Q2 0.27193465 0.043144161 -0.622532626 0.05287344 -0.005544014
## 20 11 Q3 0.47191832 -0.264881208 0.009175851 0.92601146 0.069708752
## 2011 Q4 -0.24904992 -0.003456839 0.144084958 -0.62562092 0.028597598
## 2012 Q1 0.35855743 0.069705675 -0.076753493 0.59222442 0.035646285
## 2012 Q2 -0.01474392 -0.168646735 -0.153590576 -0.10019918 -0.082839750Forcasting
forecast_result <- predict(var_from_vecm, n.ahead = 8, ci = 0.95)
# Plot forecast
plot(forecast_result)
##
## Forecast values (8 quarters ahead):## $SS
## fcst lower upper CI
## [1,] 1.605694 0.7479494 2.463439 0.8577446
## [2,] 1.611751 0.4336166 2.789886 1.1781347
## [3,] 1.586620 0.1371140 3.036127 1.4495065
## [4,] 1.575733 -0.1251618 3.276628 1.7008948
## [5,] 1.575254 -0.3553441 3.505852 1.9305980
## [6,] 1.573707 -0.5637094 3.711122 2.1374159
## [7,] 1.573379 -0.7538937 3.900652 2.3272729
## [8,] 1.573031 -0.9301532 4.076216 2.5031844
##
## $RD
## fcst lower upper CI
## [1,] 1.010021 0.4626479 1.557394 0.5473729
## [2,] 1.198063 0.4363986 1.959727 0.7616644
## [3,] 1.119401 0.1308119 2.107990 0.9885888
## [4,] 1.124661 -0.0168723 2.266194 1.1415329
## [5,] 1.123182 -0.1529811 2.399344 1.2761628
## [6,] 1.122848 -0.2760455 2.521741 1.3988931
## [7,] 1.123058 -0.3881106 2.634226 1.5111683
## [8,] 1.122517 -0.4933669 2.738400 1.6158837
##
## $Inflasi
## fcst lower upper CI
## [1,] -1.360096 -2.426200 -0.29399141 1.066104
## [2,] -1.406947 -2.832335 0.01844013 1.425387
## [3,] -1.422497 -3.151050 0.30605525 1.728552
## [4,] -1.414617 -3.398196 0.56896172 1.983579
## [5,] -1.422962 -3.632680 0.78675654 2.209718
## [6,] -1.421232 -3.837504 0.99504099 2.416273
## [7,] -1.422686 -4.028842 1.18346908 2.606156
## [8,] -1.422406 -4.205838 1.36102592 2.783432
##
## $IHSGr
## fcst lower upper CI
## [1,] 0.27439821 -1.774880 2.323677 2.049278
## [2,] 0.02429745 -2.072218 2.120813 2.096516
## [3,] 0.04022440 -2.085499 2.165947 2.125723
## [4,] 0.03617014 -2.128068 2.200409 2.164238
## [5,] 0.03681954 -2.160124 2.233763 2.196943
## [6,] 0.04127901 -2.189411 2.271969 2.230690
## [7,] 0.03851103 -2.223840 2.300862 2.262351
## [8,] 0.03987593 -2.254377 2.334129 2.294253
##
## $PDB
## fcst lower upper CI
## [1,] 1.867036 1.682400 2.051671 0.1846354
## [2,] 1.845104 1.533872 2.156336 0.3112317
## [3,] 1.837949 1.414088 2.261810 0.4238611
## [4,] 1.835734 1.313495 2.357973 0.5222390
## [5,] 1.834543 1.226102 2.442984 0.6084411
## [6,] 1.833916 1.148585 2.519246 0.6853308
## [7,] 1.833690 1.078664 2.588716 0.7550260
## [8,] 1.833582 1.014533 2.652632 0.8190496Forecast Eror Matrix
for(var in names(forecast_result$fcst)){
cat("\n--- Forecast for", var, "---\n")
print(forecast_result$fcst[[var]])
}##
## --- Forecast for SS ---
## fcst lower upper CI
## [1,] 1.605694 0.7479494 2.463439 0.8577446
## [2,] 1.611751 0.4336166 2.789886 1.1781347
## [3,] 1.586620 0.1371140 3.036127 1.4495065
## [4,] 1.575733 -0.1251618 3.276628 1.7008948
## [5,] 1.575254 -0.3553441 3.505852 1.9305980
## [6,] 1.573707 -0.5637094 3.711122 2.1374159
## [7,] 1.573379 -0.7538937 3.900652 2.3272729
## [8,] 1.573031 -0.9301532 4.076216 2.5031844
##
## --- Forecast for RD ---
## fcst lower upper CI
## [1,] 1.010021 0.4626479 1.557394 0.5473729
## [2,] 1.198063 0.4363986 1.959727 0.7616644
## [3,] 1.119401 0.1308119 2.107990 0.9885888
## [4,] 1.124661 -0.0168723 2.266194 1.1415329
## [5,] 1.123182 -0.1529811 2.399344 1.2761628
## [6,] 1.122848 -0.2760455 2.521741 1.3988931
## [7,] 1.123058 -0.3881106 2.634226 1.5111683
## [8,] 1.122517 -0.4933669 2.738400 1.6158837
##
## --- Forecast for Inflasi ---
## fcst lower upper CI
## [1,] -1.360096 -2.426200 -0.29399141 1.066104
## [2,] -1.406947 -2.832335 0.01844013 1.425387
## [3,] -1.422497 -3.151050 0.30605525 1.728552
## [4,] -1.414617 -3.398196 0.56896172 1.983579
## [5,] -1.422962 -3.632680 0.78675654 2.209718
## [6,] -1.421232 -3.837504 0.99504099 2.416273
## [7,] -1.422686 -4.028842 1.18346908 2.606156
## [8,] -1.422406 -4.205838 1.36102592 2.783432
##
## --- Forecast for IHSGr ---
## fcst lower upper CI
## [1,] 0.27439821 -1.774880 2.323677 2.049278
## [2,] 0.02429745 -2.072218 2.120813 2.096516
## [3,] 0.04022440 -2.085499 2.165947 2.125723
## [4,] 0.03617014 -2.128068 2.200409 2.164238
## [5,] 0.03681954 -2.160124 2.233763 2.196943
## [6,] 0.04127901 -2.189411 2.271969 2.230690
## [7,] 0.03851103 -2.223840 2.300862 2.262351
## [8,] 0.03987593 -2.254377 2.334129 2.294253
##
## --- Forecast for PDB ---
## fcst lower upper CI
## [1,] 1.867036 1.682400 2.051671 0.1846354
## [2,] 1.845104 1.533872 2.156336 0.3112317
## [3,] 1.837949 1.414088 2.261810 0.4238611
## [4,] 1.835734 1.313495 2.357973 0.5222390
## [5,] 1.834543 1.226102 2.442984 0.6084411
## [6,] 1.833916 1.148585 2.519246 0.6853308
## [7,] 1.833690 1.078664 2.588716 0.7550260
## [8,] 1.833582 1.014533 2.652632 0.8190496